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We construct a Madelung fluid model with specific time variable parameters asdissipative quantum fluid and linearize it in terms of Schrodinger equationwith time dependent parameters. It allows us to find exact solutions of thenonlinear Madelung system in terms of solutions of the Schrodinger equation andthe corresponding classical linear ODE with variable frequency and damping. Forthe complex velocity field the Madelung system takes the form of a nonlinearcomplex Schrodinger-Burgers equation, for which we obtain exact solutions usingcomplex Cole-Hopf transformation. In particular, we discuss and give exactresults for nonlinear Madelung systems related with Caldirola-Kanai typedissipative harmonic oscillator.

Madelung Representation and Exactly Solvable Schrodinger-Burgers Equations with Variable Parameters